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Block #211,961

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/16/2013, 12:06:45 AM Β· Difficulty 9.9180 Β· 6,589,597 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
1b06542d941bb9e103f134c809bdeee9be0e93137018f9977708dbd92a25cde2
View on Chainz β†—

Height

#211,961

Difficulty

9.917998

Transactions

2

Size

687 B

Version

2

Bits

09eb01e7

Nonce

45,245

Timestamp

10/16/2013, 12:06:45 AM

Confirmations

6,589,597

Mined by

⛏️ P2SHAaC7FfYJ3wgrxGC78ZvTmB5mToNd6BeiX3

Merkle Root

7c9d332e87754381ce74549a446bd82b63c766702a24403bf0d837b6711a7887
Transactions (2)
Coinbase7274d0a87e863f…3555b071c1a77a
1 in β†’ 1 out10.1600 XPM109 B
AaC7FfYJ…Nd6BeiX3
a60eda48afe2c4…4a2ff9edad12d9
3 in β†’ 1 out150.0000 XPM487 B
AL9QYT6h…EExU8BRE
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.717 Γ— 10⁹⁷(98-digit number)
17172564859023776096…53253562972514540181
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
1.717 Γ— 10⁹⁷(98-digit number)
17172564859023776096…53253562972514540181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.434 Γ— 10⁹⁷(98-digit number)
34345129718047552192…06507125945029080361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.869 Γ— 10⁹⁷(98-digit number)
68690259436095104385…13014251890058160721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.373 Γ— 10⁹⁸(99-digit number)
13738051887219020877…26028503780116321441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.747 Γ— 10⁹⁸(99-digit number)
27476103774438041754…52057007560232642881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.495 Γ— 10⁹⁸(99-digit number)
54952207548876083508…04114015120465285761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.099 Γ— 10⁹⁹(100-digit number)
10990441509775216701…08228030240930571521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.198 Γ— 10⁹⁹(100-digit number)
21980883019550433403…16456060481861143041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.396 Γ— 10⁹⁹(100-digit number)
43961766039100866806…32912120963722286081
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,656,544 XPMΒ·at block #6,801,557 Β· updates every 60s
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